In section  the Lagrangian governing the hidden field dynamics just consists of a Maxwell term plus a real scalar field so that there is no gauge symmetry breaking in this sector. Nevertheless, the mixing Lagrangian, apart from KM and SGI interactions includes a potential mixing between visible and hidden scalar fields in such a way that the latter develops a non-zero value at the origin, which can be associated with a scalar condensate, a phenomenon of interest already studied in the context of cosmic strings [1]} and also topological defects [2]}, [3]}, [4]}, additionally is particularly relevant in condensed matter physics and as a dark matter production mechanism.
In section  we comment on our results and we discuss possible physical implications of the models in connection with dark matter and gravitational radiation issues.
